Discovered or Invented?

This sage advice was given to me some years ago by the mother of one of my students. The boy had Aspergers Syndrome.

Had I known that division by zero would come as a surprise, I would have introduced the concept more cautiously. After leaping up with a shout and throwing his chair at his nearest classmate, he picked up his desk ready to smash a window. And no, I’m not exaggerating. ‘Settle down,’ I yelled. ‘And let me explain why it’s not often zero.’

The world of mathematics with its consistent rules and its ‘right’ answers is a great comfort to the average Aspergers kid.

(There’s a modern philosophy afoot in some schools that class consensus is how an answer should be arrived at. I’ve even heard of some kids who’ve been labelled ‘bigots’ for suggesting there is one and only one ‘correct’ answer. This extreme relativistic mindset is immensely stressful for kids like the one I’ve described. For them, security lies in knowing the rules, whether in mathematics or the playground. The supreme order of arithmetic reduces their anxiety considerably. Two and two always equals four—and, trust me, I’ll never even hint at the existence of those branches of mathematics where it doesn’t.)

Mathematics is a genuinely international language. It transcends borders. No matter where you go in the world 2 + 2 is still the same. (And, of course, almost always four.)

It may come as a surprise, therefore, to know that quite a few famous scientists and mathematicians are bemused by the fact that it works so well. With mathematics, we can put a man on the moon and bring him home again. With mathematics, we can predict the trajectory of a baseball, an airliner, a missile or a meteor.

When mathematicians think philosophically, this can be baffling. If mathematics is a man-made construct, there’s no reason it should be as accurate out in the real world as it is. ‘What is it,’ Stephen Hawking asked, ‘that breathes fire into the equations and makes a universe for them to describe?’

The simplest answer is: mathematics is not a man-made construct. It is discovered, not invented. It’s ‘out there’ waiting. It’s a vast realm, only partly explored.

You don’t have to have a Christian worldview to believe this. Platonic idealism is a dominant philosophy in modern mathematics, holding that there exist universal abstract forms. Today’s Platonists may not believe, as their ancient predecessors did, that numbers are gods but some come close.

It never ceases to surprise me (though, fortunately, not to the level of my Aspergers student) that so many Christians think mathematics is neutral ground. They have no idea that in the past it’s been the frontline between Christianity and Gnosticism, Christianity and Pythagoreanism, Christianity and neo-Platonism, Christianity and Hindu-Buddhist thought. The fiercest of battles have been fought with a Christian understanding of mathematics as the target.

Yet, today, most Christians have taken the postmodern view that mathematics can tell us virtually nothing about God, except in general terms. Nothing specific.

It’s an idea that’s so foreign to Biblical thinking with its Hebraic fusion of words and numbers that I find it difficult to believe how entrenched it is.

When I was much younger, I read of Eugene Shoemaker’s description of Gosse Bluff in central Australia, perhaps the only comet crater on Earth. He described the waveprint in the rock as a message from the moment of impact, preserved across countless ages. ‘What message,’ I wondered, ‘would be so important that God would write it in stone?’

I’ve been to Gosse Bluff and seen those shattercones Shoemaker described. Curiously they have the same mathematics as the song of the Crab Nebula, the partition of Saturn’s rings, the core of an apple I just ate and the chapter of Genesis I read this morning.

Creation is as specific in its testimony as Scripture. It’s not as comprehensive but it’s not vague. Recently the idea that any mathematical interpretation of Scripture or Creation is numerological raised its head—yet again.

I find this attitude like that of the kids who find an answer by consensus. It’s a pooling of ignorance by those who take a quick look on Google and think they know as much as someone who has spent a decade in study.

Everywhere, absolutely everywhere, the silent shout of creation is: ‘God is a Trinity, God is love, God is resurrection and life.’

It’s hard to convince people of this. So, until I run out of copies, if you comment and ask for a copy of The Singing Silence I’ll send one to you free.

6 Comments

I think that to be born into a world and then think that you can somehow be part of the forming of its essence is arrogance in its highest form. People can believe that different answers exist, but like the law of gravity, eventually what is real will catch up with them.

May God bring clear thinking back to this world of warped ideas…
Alison Collins

Allison, you know I think that clear thinking does exist and shines very brightly in the awful downward-spiralling darkness. My belief is that this is because the world is nearing its consummation. Your prayer will be answered when He returns! The truth will overtake people who are willingly ignorant, I believe. God will be glorified in His Son!

…and yet there is a degree to which we do form the world. I look back on the ancient Hebrew concept that words were living things that, once spoken, could not be recalled and I wonder about this day and age. Do writers of books and movies reflect the culture or create it? That’s not an easy question to wrestle with.

Tolkien spoke of humanity as ‘sub-creators’ made in the image of God the Creator. If we do create our culture (and not just books or artwork or technology), then we have an incredible responsibility.

At least, some of us feel we do. For others, freedom of expression is far more important than any notion of responsibility.

Anne, this is a very interesting post. Today I spoke with a woman whose 15-year-old son has Aspergers, and she explained some of what this means for both of them. I overheard this boy telling someone that he was good at science and so was going to stick with science. Perhaps that’s because order and design are innate in the world, and he thrives on order, and disorder or surprises upset him. Anyway, he and his Mom seem to be doing well. She is a godly woman who is grateful that her other children are grown and thus she can spend time with this younger child who has special needs.

I’m intrigued by your statement that the Creation is a witness to the Triune nature of God (and other things about Him too). Wow! Science was never my strong suit–I wanted to be IMAGINING not DISCOVERING. But as I get older the real world becomes more of what it really is–amazingly interesting, and so I’m becoming a very amateur but grateful naturalist/oberserver.

I should mention that the boy in my story stayed in my class for four years (I discovered later because his mum especially requested it) and when he finally moved on, she came to thank me. She said he’d enjoyed my classes so much and partly that was because I’d never surprised him. I told her that I had once – but only once! I didn’t tell her that I learned to anticipate what might cause trouble. Every time there was an unusual result looming, I’d preface it with, ‘Now, don’t be surprised by the result we’re about to find. It may look strange at first but we’ll look at the reason why shortly.’

I’ve come to the point where I think imagining IS discovering. I was writing a fantasy which was threatening to become a monster brick in size and, in an attempt to keep the word count under control, I restructured it three times totally even before I got to the end of it. From scratch. I became curious that every time I did this that the only thing that remained intact was a number. So I imagined an entire empire of mathematics built around this number which I called the Mathematics of If. I used this dodgy product of my imagination to enable the Wise Men to calculate the time and location of the birth of the Jewish Messiah. And when I finished the book and decided to remove this (because surely it couldn’t work!), I was astonished to discover that I had imagined a number that could define the latitude of Bethlehem. No GPS required.

This was a watershed for me. I treat my imagination seriously. And I treat other people’s seriously as well. I believe it is possible to discover via imagining. There are patterns most people never see because they’ve already made up their minds that there is nothing to see. This is true in fiction as much as the ‘real’ world.

Anne, first, let me apologize for not responding to this. I thought I’d subscribed to your blog, but have got something wrong. With no experience in following blogs through feeds, I’ve somehow missed this.

Anyway, this young man had a happy experience then in being taught by a teacher willing to understand and meets his needs. That’s great! That experience became part of who he is.

You went to great lengths to shorten the fantasy book. Did you think we would want a shorter book? You may have been wrong. MANY-COLOURED REALM is most unusual, wonderful! Probably there is much that’s going over my head, in the way of numbers, but I’m enjoying it thoroughly!

So, you are saying that you believe we discover by imagining. This makes sense to me as far as emotional, psychological, and intuitive matters go; that I get. We get to create and ‘know’ characters and recieve many insights about them, and insights through plot and world-building. I guess it also makes sense in science, because it’s your experience and the experience of other scientific minds, so I’ve heard. How could we ever THINK without it? The latitude of Bethlehem? That’s amazing and good.